Effects of A Nonrandom Sample

Effects of A Nonrandom Sample

Math Test Scores

Opening

Math Test Scores

Every seventh grade student (870 total) in a school district takes the same math test. "X" represents one student in Class A. Based on the sample of Class A’s test results, how did all of the seventh graders in the district do on the test?

  • Think about the question. Then discuss your ideas with a partner.

Math Mission

Opening

Analyze samples to make generalizations about a population.

Make Generalizations About a Population

Work Time

Make Generalizations About a Population

Use these test results for Class A to describe the seventh graders in the district (870 total).

Think of all the tools you can use to describe and analyze data—measures of center, measures of spread, line plots, box plots, and histograms—and how you might use these tools in this problem.

"X" represents one student in Class A.

Answer the following questions:

  • Which tools do you think will be most helpful to you?
  • What is the typical score on the district math test? How can you show this?
  • Where do the middle 50% of the scores lie?
  • About how many seventh grade students in the district would have the typical score?
  • About how many seventh grade students would have each of the scores?
  • What are some of the tools you can use to analyze data?
  • Have you tried using any of the graphing tools?
  • How many data points are on the line plot?
  • How does that number compare to the total number of seventh grade students in the district?
  • Does the sample represent the population of the district?

A Second Sample

Work Time

A Second Sample

Here is data from another seventh grade class, Class B, in the same district.

"X" represents one student in class B.

  • What does this sample tell you about the first sample?
  • How can you use this sample to help you make a better generalization about the population?

Prepare a Presentation

Step 1: Work Time

Prepare a Presentation

  • Prepare a presentation about your conclusions for the results of all the seventh graders in the district.
  • State how certain you are about your conclusions, and support your thinking with evidence.

Step 2: Work Time

Challenge Problem

  • How could you get a representative random sample of all the seventh grade results?

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about the different approaches your classmates used to describe and make conclusions about the data.

As your classmates present, ask questions such as:

  • Which value is a better indicator of the typical score—the mean, median, or mode? Why?
  • Where is the data clustered on the line plot? What is the range of the data?
  • What does this information tell you about the data, and possibly the sample?
  • What is a typical score for Class A? For Class B?
  • Based on the line plots, which class performed better on the test? How do you know?
  • Are either of these samples a random sample? Explain.
  • Would you consider the combined results of the two samples to be a random sample?
  • Are the combined class results closer than the separate class results to showing how all the seventh graders in the district did on the test? Explain.

Analyzing Samples

Formative Assessment

Summary of the Math: Analyzing Samples

Write a summary about analyzing and describing samples.

Check your summary.

  • Do you list some of the tools available for analyzing data?
  • Do you explain how you can use these tools to analyze a sample?
  • Do you explain what a sample tells you about the population?

Reflect on Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

When I look at a graph, I can tell these things about the data…